Dynamical systems of scalar fields in f(Q,C) gravity

Abstract

This paper investigates the dynamics of a scalar field within the framework of modified gravity, specifically using the $f(Q,C)$ formalism, through a dynamical system approach. We investigate a particular scalar potential, $V\left(\varphi \right)=V_{0}sin{h}^{-\alpha }\left(\beta \varphi \right)$ and derive the associated autonomous system of equations, which describes the dynamics and characteristics of the scalar field. We examine the fixed points to understand the stability and behavior of cosmological solutions, particularly the transition from decelerated to accelerated expansion. Our analysis reveals that six fixed points for non-interacting scenario represent stable configurations which indicate dark energy-dominated phases and the other fixed points represent saddle behavior which indicate the matter-dominated phases of the Universe. The analysis reveals that the scalar field in $f(Q,C)$ gravity provides a natural mechanism for the Universe's accelerated expansion at late times. The Universe's accelerated expansion which is fueled by dark energy, is supported by our model in which the transition redshift and the current values of the deceleration and equation of state parameters are found as $z_{tr}\approx 0.654$, $q_0=-0.546$ and ${\omega }_0=-1.0132$ respectively. Our model exhibits excellent consistency with observational datasets, such as Hubble and Supernovae data sets which affirm its capability to offer fresh perspectives on the accelerating Universe. Finally, we discuss the broader implications of this model for the late-time evolution of the Universe and highlight potential areas for future research.